Terwilliger systems' subdegree bound conjecture

Let $\Phi$ be a TD system with diameter $d$, and let $\rho_0,\rho_1,\ldots,\rho_d$ be the associated scalars from Corollary 3.4. The scalars satisfy

$$\rho_i\leq \binom{d}{i}\qquad (0\leq i\leq d).$$

Terwilliger systems' subdegree bound conjecture. The inequality above holds for every TD system.

This conjecture gives an upper bound on the associated scalars in terms of the diameter. It has been proved for $d\leq 3$ by Tanabe; its validity in general remains open.